Mobile First Indexing Enabled - Webmaster Tools

Just started getting this message from Google for all my websites registered with GWT:

Mobile-first Indexing Enabled
"This means that you may see more traffic in your logs from Googlebot Smartphone. You may also see that snippets in Google Search results are now generated from the mobile version of your content.

Background: Mobile-first indexing means that Googlebot will now use the mobile version of your site for indexing and ranking, to better help our (primarily mobile) users find what they're looking for. Google’s crawling, indexing, and ranking systems have historically used the desktop version of your site's content, which can cause issues for mobile searchers when the desktop version differs from the mobile version. Our analysis indicates that the mobile and desktop versions of your site are comparable.

For more information:
• Monitor your index coverage using the Index Status report.
• Monitor your impressions, clicks, and site appearance using the Performance report.
• If you have any additional questions, drop by our Webmaster forum for more help - mention message type [WNC-****] or our public events."

Does anybody know just how this will affect rankings? I use responsive themes and amp pages already, haven't seen this discussed yet and wonder if this will negatively affect SEO or what's exactly going on here. Anything to worry about?

I've received the same message for several of my websites but I didn't give it much importance, let's see what the experts say...

This is one of the latest news of the google - it's been announced a long time ago, but they are already beginning to impose it. On what I read, the index will be first for mobile - so far it was for a desktop. This means that only the mobile version will be ranked - if you have text on the desktop version, but you do not have it on the mobile - the text will not play a role in the ranking. Can anyone more familiar to explain how he/she understood this for mobile-first index?